# Identify Direct Proportion and Solve Simple Problems

In this worksheet, students will use information relating to groups of items to find the cost of a single item, then apply this to find the value of a differently-sized new group or to identify the best value for money.

Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Ratio, Proportion and Rates of Change Direct and Inverse Proportion

Difficulty level:

#### Worksheet Overview

The easiest way to solve all problems involving direct proportion is to start by finding the value of a single unit.

Let's look at this process in action in some examples below before we tackle some related questions.

e.g. If 8 pens cost £5.28, what is the cost for 5 pens?

Firstly, we need to find the cost of 1 pen.

We can lay out our findings in a table like this:

 Pens Cost 8 £5.28 1 £5.28 ÷ 8 £0.66 5 £0.66 × 5 £3.30

e.g. 12 blocks of cheese make sandwiches for 48 people.

How many people can sandwiches be made for with 30 blocks of cheese?

Firstly, let's find out how many sandwiches can be made from 1 block of cheese:

1 block will make 48 ÷ 12 = 4 sandwiches

So 30 blocks of cheese will make sandwiches for:

30 × 4 = 120 people

Now you have a pen and a cheese sandwich, it's time to solve some problems using these skills!

In this activity, we will use information relating to groups of items to find the cost of a single item, then apply this to find the value of a differently-sized new group or to identify the best value for money.

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